Shed Floor Replacement

I posted a thread about this earlier and was told to buy a toe kick saw and cut as close to the 2x4's that make the exterior walls of the shed. The more I think about this the more I wonder if I wont be creating weak spots on the new floor. Let me explain:

Lets say I start in one corner and cut all the way to the 2x4's. When I screw down new plywood wouldn't there be inherent weak spots right next to those 2x4's because there wouldn't be anything immediately underneath to screw to (unless the joists happen to be right there which I believe is unlikely)?

I'm guessing this would make more sense with pictures but since I haven't started yet its hard. I've got one pic from the previous thread that I'm attaching to give you an idea of what I'm working with.

Any help would be appreciated. I likely wont start this for another week or two...plenty of time for the collective wisdom of this forum to help me out.

Attached Thumbnails

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Just add some blocking. A 2 X 6 laying flat up under the space between the joist and attached to the bottom of the walls will cover the gap and give you something to attach the flooring to.
If that was mine and was replacing the floor, I'd take the time to remove whole door and cut the new subfloor so it runs where the threshold sits.
That's the most important weak spot.
I'd also add the missing flashing under the door before the floor rots.http://www.bing.com/images/search?q=...lectedIndex=25

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Well I guess if I'm going to do it, now would be the best time to do it since I've got the door frame exposed. I am not sure who built this shed and for what purpose it originally was intended, but plenty of things about it did not make sense when I started.

The previous owner had buried (in conduit) cable to run power to the shed but never hooked it up. He mounted an A/C in the shed though there was no power. Finally he had (*as the previous picture shows) the blue R3 foam insulation screwed on the inside of the walls using dry wall screws (all of this has since been removed). He had the R3 holding up (very poorly) regular insulation in between the studs as well. I have no idea how he ever intended to get sheetrock to stay up on the walls with all the insulation.

The door wouldn't be that bad to remove and frankly I have questions as to whether it is truly square or not (the door sticks a bit on closing). Removing it would allow me to flash underneath it, cut the floor out properly and then re-install the door properly.